We see that all of the auxiliary,
intermediate Hilbert spaces
\({\cal R}_j\)  with \(0<j<{K-1}\)  have been successfully eliminated.
In terms of the operator-product metric \(\Theta _2\) 
the observability of \(H\)  is fully guaranteed, strictly
in the spirit of review [1]},
by
its quasi-Hermiticity property (REF ) in \({\cal H}_{math}\) .
A consistent quantum model
can be constructed
in which all observables \(\Lambda \)  would
have to satisfy the
same quasi-Hermiticity relation as \(H\)  itself does.
Besides \(Z_0\) , as we already mentioned, also operator
\(Z_1\)  represents an observable
quantity [for proof it is sufficient to
pre-multiply the underlined equation in Eq. (REF )
by \(Z_1\)  from the right]. Analogously, the product
\(Z_2\,Z_1\)  can represent another observable (the proof is similar)
while
\(Z_2\) , when standing alone, cannot.
